What is the minimum frequency to keep the mass moving?

In summary, the mass will need to move at a frequency greater than the gravitational force to keep it from being pulled down to the bottom of the circle.
  • #1
Smartgurl
15
0

Homework Statement


A mass of 2.0 x 10^2 g is tied to a 1.6 m long string and spun in a vertical circle. What is the minimum frequency to keep the mass moving?

Homework Equations


Fc=m4(pie)rf^2

The Attempt at a Solution


I know I have to use this equation and make it equal to another to find Fc however I don't know which other equation.
 
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  • #2
Well, perhaps this isn't done in outer space but on earth...
 
  • #3
Smartgurl said:
Fc=m4(pie)rf^2
That equation is not quite right. (And it's spelt pi, not pie.)
 
  • #4
haruspex said:
That equation is not quite right. (And it's spelt pi, not pie.)
Is the equation Fc = m4(pi)^2rf^2
 
  • #5
Smartgurl said:
Is the equation Fc = m4(pi)^2rf^2
Yes.
Now what about BvU's point? You need to consider gravity.
 
  • #6
haruspex said:
Yes.
Now what about BvU's point? You need to consider gravity.
Would Fg = Fc?
So I could get mg = m4(pi)^2rf^2. Then solve for f?
 
  • #7
Smartgurl said:
Would Fg = Fc?
So I could get mg = m4(pi)^2rf^2. Then solve for f?
Yes, but is that just a lucky guess or can you mount an argument to say it should be that?
 
  • #8
haruspex said:
Yes, but is that just a lucky guess or can you mount an argument to say it should be that?
I drew a diagram and I think that when the mass is at the top it will need the minimum Fc as gravity will help bring it down. Where at the bottom the Fc will have to overcome gravity to bring the mass back up. So gravity will be the only force acting on the mass and bringing it down when it is at the top.
 
  • #9
Smartgurl said:
I drew a diagram and I think that when the mass is at the top it will need the minimum Fc as gravity will help bring it down. Where at the bottom the Fc will have to overcome gravity to bring the mass back up. So gravity will be the only force acting on the mass and bringing it down when it is at the top.
Good.
 
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  • #10
haruspex said:
Good.
Thank you so much! Now it seems simple since I understand it
 

Related to What is the minimum frequency to keep the mass moving?

1. What is frequency in relation to mass movement?

Frequency refers to the number of oscillations or cycles that occur in a given time period. In the context of mass movement, it is the number of times an object moves back and forth in a specified amount of time.

2. How does frequency affect mass movement?

The higher the frequency, the faster the mass will move. This is because a higher frequency means that more oscillations are occurring in a given time period, resulting in a greater movement of the mass.

3. What is the minimum frequency needed to keep the mass moving?

The minimum frequency needed to keep the mass moving depends on various factors such as the mass of the object, the surface it is moving on, and the external forces acting on it. In general, a minimum frequency of at least one oscillation per second is needed to keep the mass in motion.

4. How does frequency relate to the concept of resonance?

Resonance occurs when the frequency of an external force matches the natural frequency of an object. This results in a significant increase in the amplitude of the object's movement. Therefore, frequency plays a crucial role in resonance and can greatly impact the movement of objects.

5. Can the frequency of an object's movement change?

Yes, the frequency of an object's movement can change depending on the external forces acting on it. For example, if a force is applied to an object, it will experience a change in its frequency of movement. Additionally, the frequency can also change if the mass of the object is altered.

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